Cost-effectiveness measures on convex and nonconvex technologies

Camanho and Dyson (2005) extended Shephard's (1974) revenue-indirect cost efficiency approach to a cost-effectiveness framework, which helps to assess the ability of a firm to achieve the current revenue (expressed in the firm's own prices and quantities) at minimum cost. The degree of cost-effectiveness is quantified as the ratio of the minimum cost to the observed cost of the evaluated firm where the minimum cost is computed by simultaneously adjusting the output levels at the current revenue. In this paper, we develop two cost-effectiveness approaches based on convex data envelopment analysis and nonconvex free disposable hull technologies. The objectives of this paper are threefold. Firstly, we develop a convex cost-effectiveness (CCE) measure which is equivalent to the Camanho-Dyson CCE measure under the constant returns-to-scale assumption. Secondly, we introduce three nonconvex cost-effectiveness (NCCE) measures which are shown to be equivalent with respect to each returns-to-scale nonconvex technology. Finally, we apply our framework to a real data.